

A202604


Clique number for the nKeller graph.


4



1, 2, 5, 12, 28, 60, 124, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824, 2147483648, 4294967296, 8589934592
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OFFSET

1,2


COMMENTS

a(n) <= 2^n.
a(7) = 124 was established by Debroni et al. (2011).
a(8) = 2^8 was established by Mackey (2002).
a(n) = 2^n for n >= 8 (see Jarnicki et al.).


LINKS

Colin Barker, Table of n, a(n) for n = 1..1000
J. Debroni, J. D. Eblen, M. A. Langston, P. Shor, W. Myrvold, D. Weerapurage, A complete resolution of the Keller maximum clique problem, Proceedings of the 22nd ACMSIAM Symposium on Discrete Algorithms, pp. 129135, 2011.
Witold Jarnicki, W. Myrvold, P. Saltzman, S. Wagon, Properties, Proved and Conjectured, of Keller, Mycielski, and Queen Graphs, arXiv preprint arXiv:1606.07918 [math.CO], 2016.
J. Mackey, A cube tiling of dimension eight with no facesharing, Discrete & Computational Geometry 28 (2): 275279, 2002.
Eric Weisstein's World of Mathematics, Clique Number
Eric Weisstein's World of Mathematics, Keller Graph
Index entries for linear recurrences with constant coefficients, signature (2).


FORMULA

G.f.: x*(1 + x^2 + 2*x^3 + 4*x^4 + 4*x^5 + 4*x^6 + 8*x^7) / (1  2*x).  Colin Barker, Oct 14 2017


MATHEMATICA

Table[Piecewise[{{1, n == 1}, {2, n == 2}, {5, n == 3}, {2^n  4, 4 <= n <= 7}}, 2^n], {n, 20}] (* Eric W. Weisstein, Mar 21 2018 *)
Join[{1, 2, 5, 12, 28, 60, 124}, LinearRecurrence[{2}, {256}, 14]] (* Eric W. Weisstein, Mar 21 2018 *)
CoefficientList[Series[(1  x^2  2 x^3  4 x^4  4 x^5  4 x^6  8 x^7)/(1 + 2 x), {x, 0, 20}], x] (* Eric W. Weisstein, Mar 21 2018 *)


PROG

(PARI) Vec(x*(1 + x^2 + 2*x^3 + 4*x^4 + 4*x^5 + 4*x^6 + 8*x^7) / (1  2*x) + O(x^40)) \\ Colin Barker, Oct 14 2017


CROSSREFS

Cf. A295902, A296100, A296101.
Sequence in context: A316706 A171579 A228638 * A118898 A111586 A192657
Adjacent sequences: A202601 A202602 A202603 * A202605 A202606 A202607


KEYWORD

nonn,easy


AUTHOR

Eric W. Weisstein, Dec 21 2011


EXTENSIONS

More terms from N. J. A. Sloane, Jul 04 2017 based on the Jarnicki et al. survey.


STATUS

approved



